Question 1 Refer to the Taz Notes file posted to canvas and your class notes. Recall that our exxpression for the welfare cost of a tax in the final goods market for X can be written as WC = %Axn (1) where WC is the change in total surplus, T} is the excise tax on X, and AX is the change in X following the price increase caused by the tax. We showed that we can find AX by taking the total derivative of the demand equation for X: 0X AX = AdP,. 2 2P, (2) In equation 2, 837{2 is the slope of the demand curve and dF, is the magnitude change in the price, or T}, in the case of an excise tax. Rewriting expression 2 we have 0X AX = T,. 3 5P, 3) and by substituting (3) into (1) we have 19X WC =-_-T2 4 For 1a to 1c you will find the expression for the welfare costs under different functional forms for demand. Compute 6%' and substitute that into the WC formula in equation 4. Simplify as much as possible and answer the follow-up questions. For help with computing partial derivatives, use this source: . . Show your steps, and remember by law of demand g%z is always negative. la. Linear case. For the demand curve X=a-bF, write the expression for the welfare cost of an excise tax T,. Then, compute the lost gains from trade if a=20, b=>5, and 1} = 2. 1b. Non-Linear case #1. For the demand curve X =a-In(P,) where In(P,) is the natural log of the price. Write the expression for the welfare cost of an excise tax T,. In words, what is the ratio %? From your solution, are lost gains from trade increasing or decreasing in this ratio? 1c. Non-Linear case #2. For the demand curve X=a-F; 1 Note that /P, can also be written P? Write the expression for the welfare cost of an excise tax T),. Ceteris parabus, will lost gains from trade be higher if P, = 10 or P, = 127